After finishing Q3 of a1, I had lingering thoughts about a certain part of the proof - I wasn't fully convinced that it works. I kept wondering if I needed induction to justify the implication, or if doing that is unnecessary and what I have is sufficient.
A dose of the very helpful Danny's Office Hour gave me the answer.
So, I believe the lesson today is that if I'm not fully convinced myself, I need to do more work on justifying the part of concern.
Danny also pointed out some problems with "big jumps" and generality issues. I think I had an idea of what he meant, but wasn't entirely sure.
As I worked on adding the induction proof, I encountered very similar generality issues, having to do with fundamental definitions of natural numbers, integers. It was then that I realized what Danny meant, and understood the importance of these fundamental definitions that I never really internalized.
So, the second lesson today is, even if I feel like I'm convinced, it may not be due to correct understanding, and so it's a good idea to visit Danny or a TA to check my works.
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